Toward a well-founded theory for multi-level conceptual modeling

Multi-level conceptual modeling addresses the representation of subject domains dealing explicitly with multiple classification levels. Despite the recent advances in multi-level modeling techniques, we believe that the literature in multi-level conceptual modeling would benefit from a theory that: (1) formally characterizes the nature of classification levels and (2) precisely defines the structural relations that may occur between elements of different classification levels. This work aims to fill this gap by proposing an axiomatic theory that can be considered a reference top-level ontology for types in multi-level conceptual modeling. The theory provides the modeler with basic concepts and patterns to articulate domains that require multiple levels of classification as well as to inform the development of well-founded languages for multi-level conceptual modeling. The whole theory is founded on a basic instantiation relation and characterizes the concepts of individuals and types , with types organized in levels related by instantiation. Further, it includes intra-level structural relations that are used to define expressive multi-level models and cross-level relations that allow us to account for and incorporate the different notions of power type in the literature.